Discrete-time analog filter

ABSTRACT

A discrete-time analog filter, where a filter tap of the filter comprises a voltage-to-current converter, an active current mirror, and a current multiplier to provide a current signal indicative of a weighted sampled voltage signal. The current signals from the filter taps are summed by one or more active cascode differential latches to provide an output logic signal indicative of the filtered output. The discrete-time analog filter finds applications in channel equalization, and is suitable for high data rates and low voltage applications. The voltage and current signals may be differential. The voltage-to-current converter may include a common-mode high-pass filter to reject common-mode voltage variations.

FIELD

[0001] Embodiments of the present invention relate to analog circuits, and more particularly, to discrete-time analog filters.

BACKGROUND

[0002]FIG. 1 provides a high-level abstraction of a portion of a computer server or system, where microprocessor 102 resides on board 104 and communicates with memory 106 on board 108. The communication is by way of striplines on backplane 110. Backplane 110 is connected to boards 104 and 108 by connectors 112. Not shown in FIG. 1 are other memory units and microprocessors, where the various microprocessors and memory units may communicate to one another so as to access or write data and instructions.

[0003] Communication of signals over backplane 110 may be modeled by transmission line theory. Often, the signaling is based upon differential signaling, whereby a single bit of information is represented by a differential voltage. For example, FIG. 2a shows drivers 202 and 204 driving transmission lines 206 and 208, respectively. For differential signaling, drivers 202 and 204 drive their respective transmission lines to complementary voltages. Typical curves for the node voltages at nodes n1 and n2 for a bit transition are provided in FIG. 2b, where the bit transition is indicated by a dashed vertical line crossing the time axis. The information content is provided by the difference in the two node voltages.

[0004] For short-haul communication, such as for the computer server in FIG. 1, the signal-to-noise ratio is relatively large. If the transmission lines are linear, time-invariant systems having a bandwidth significantly greater than that of the transmitted signal, then a relatively simple receiver architecture may be employed to recover the transmitted data. Such a receiver is abstracted by comparator 210, which provides a logic signal in response to the difference in the two received voltages at ports 212 and 214.

[0005] However, every transmission line has a finite bandwidth, and for signal bandwidths that are comparable to or exceed the transmission line (channel) bandwidth, intersymbol interference may present a problem. Furthermore, actual transmission lines may have dispersion, whereby different spectral portions of a signal travel at different speeds. This may result in pulse spreading, again leading to intersymbol interference. As a practical example, for high data rates such as 10 Gbs (Giga bits per second), the transmission lines used with backplanes or motherboards are such that intersymbol interference is present.

[0006] Channel equalization is a method in which a filter is employed at a receiver so as to equalize the channel. The use of digital filters for channel equalization is well known. However, digital filters for such applications require an analog-to-digital converter, which may be costly and difficult to implement at high data rates, and the digital filtering itself may be difficult to implement at high data rates. Consequently, there has been an interest in analog filters for channel equalization. The design of analog filters for channel equalization with high data rates such as 10 Gbs may be challenging. Furthermore, in many high performance applications, the supply voltage is scaling to lower and lower values. This further challenges the circuit designer because of the reduced voltage headroom.

BRIEF DESCRIPTION OF THE DRAWINGS

[0007]FIG. 1 is a high-level abstraction of a server system, illustrating signaling between boards via a backplane.

[0008]FIG. 2a illustrates differential signaling on two transmission lines.

[0009]FIG. 2b shows typical voltage curves representing differential signaling on the transmission lines of FIG. 2a.

[0010]FIG. 3 is a voltage-to-current converter at the circuit level.

[0011]FIG. 4 is a voltage-to-current converter and current multiplier at the circuit level to effectuate a filter tap.

[0012]FIG. 5 is an analog FIR filter of order 2 at the circuit sub-block level.

[0013]FIGS. 6a through 6 d provide timing information for the filter of FIG. 5.

[0014]FIG. 7 is a filter architecture without weight shifting.

[0015]FIG. 8 is another filter architecture without weight shifting.

[0016]FIG. 9 is a filter architecture with weight shifting, but with simplified complexity.

[0017]FIG. 10 provides timing information for the filter architecture of FIG. 9.

[0018]FIG. 11 is an active cascode differential latch at the circuit level.

[0019]FIG. 12 is a comparator employing the active cascode differential latch of FIG. 11.

[0020]FIG. 13 is a voltage-to-current converter similar to that of FIG. 3 but with current sinks and nMOSFETs.

[0021]FIG. 14 is another voltage-to-current converter at the circuit level.

[0022]FIG. 15 is a voltage-to-current converter at the circuit level with common-mode voltage rejection.

[0023]FIG. 16 is a filter tap with a folded architecture.

DESCRIPTION OF EMBODIMENTS

[0024]FIG. 3 provides at the circuit level a voltage-to-current (V-I) converter according to an embodiment of the present invention. A differential voltage signal is applied to input ports 302 and 304. Current source 306 provides bias current to a diferential pair comprising pMOSFETs 308, 310, 312, and 314. The gates of pMOSFETs 308 and 310 are connected to input port 302, and the gates of pMOSFETs 312 and 314 are connected to input port 304. The combination of pMOSFET 308 to pMOSFET 310 looks like a classical cascode pair, save for the fact that the gate of pMOSFET 308 is not at a fixed voltage. A similar statement applies to the combination of pMOSFET 312 and pMOSFET 314. Accordingly, the V-I converter of FIG. 3 may be termed an active cascode V-I converter.

[0025] The betas of pMOSFET 308 and 310 may be chosen such that the active cascode configuration of pMOSFETs 308 and 310 forces pMOSFET 308 to operate in FIG. 11 he region when pMOSFET 310 is in its active region. A similar statement applies to the combination of pMOSFETs 312 and 314. This may be observed as follows. Let V_(S2) denote the source voltage of pMOSFET 310 and V_(S1) denote the source voltage of pMOSFET 308. With pMOSFET 310 in its active region, V_(S2)>V_(g)+|V_(T)|, where V_(g) is the gate voltage and V_(T) is the threshold voltage. (For simplicity, we take the threshold voltage to be the same for pMOSFET 308 and 310.) Simple manipulation of the previous inequality yields V_(GT)>V_(DS), where V_(GT) is defined as V_(S1)−V_(g)−|V_(T)| and V_(DS) is the drain-soure voltage V_(S1)−V_(S2), which indicates that pMOSFET 308 operates in its triode region.

[0026] With pMOSFETs 308 and 312 operating in the triode region, they act approximately as resistors to degenerate pMOSFETs 310 and 314, respectively. Degeneration provides a relationship between the differential input voltage V_(IN)=V₊−V⁻ and the differential current I_(OUT)=I₊−I⁻ that is linear over a wider range than if degeneration was not present. (I₊ is the drain-source current for pMOSFETs 308 and 310, and I⁻ is the drain-source current of pMOSFETs 312 and 314, respectively.) This is seen by considering a simple low frequency small-signal T-model for the active cascode V-I converter of FIG. 3, where it is easily shown that the input-output relationship between differential current and voltage is given by I_(OUT)=g_(eff)V_(IN). Here, the effective transconductance g_(eff) is given by g_(eff)=1/(r_(s)+r_(L)), where r_(s)=1/g_(m), the reciprocal of the small-signal transconductance g_(m) for pMOSFETs 310 and 314, and r_(L) is the triode region drain-source resistance for pMOSFETs 308 and 312. (For simplicity, we assume that the differential pair is matched.) If pMOSFETs 308 and 312 were not present, then the simple T-model provides I_(OUT)=g_(m)V_(IN). Clearly, g_(eff)<g_(m), so that degeneration lowers the effective transconductance. However, r_(s) is a function of the input voltage, and it is seen that because g_(eff)=1/(r_(s)+r_(L)), there is less variation in g_(eff) with input voltage than for g_(m).

[0027] It should be noted that the differential pair provided in FIG. 3 has been studied within the context of a differential amplifier, where the drains of pMOSFETs 310 and 314 are coupled to active loads. In such a case, degeneration increases the output impedance. Amplifier gain is given by the product of the effective transconductance with the output impedance. It is found that degeneration lowers the effective transconductance more than it increases the output impedance, so that amplifier gain is not increased by degeneration. However, although the active cascode differential pair of FIG. 3 may not be the best choice for amplifiers, it is proposed in these letters patent that because degeneration increases the range over which the relationship between differential voltage and current is linear, the active cascode differential pair of FIG. 3 may be effectively used with a current multiplier to perform a discrete-time analog filter.

[0028]FIG. 4 provides at the circuit level a V-I converter with current multiplier according to an embodiment of the present invention. For simplicity, only a 2-bit current multiplier is shown, but upon considering FIG. 4 and reading the description, it should be straightforward how a current multiplier for any number of bits may be implemented. The circuit of FIG. 4 comprises V-I converter 402 coupled to current multiplier 404. Current multiplier 404 may considered as a digital-to-analog converter, because the currents I_(OUT) ⁻ and I_(OUT) ⁺ at output ports 406 and 408, respectively, are analog signals modulated by the control signals D₁ and D₂ applied to the gates of the pMOSFETs in current multiplier 404. Note that {overscore (D)}₁ denotes the Boolean complement of D₁.

[0029] Current multiplier 404 shunts to ground varying amounts of current, depending upon the control signals D₁ and D₂. In the particular embodiment shown in FIG. 4, pMOSFETs 410 have a channel width-to-length ratio twice that of pMOSFETs 412. When D₁ and D₂ are both HIGH, current from V-I converter 402 is shunted to ground, and the multiplication value is zero. When D₁, is LOW and D₂ is HIGH, currents at ports 406 and 408 receive ⅓ of the currents from V-I converter 402, and the effective multiplication value is one. When D₁ is HIGH and D₂ is LOW, ⅔ of the currents from V-I converter 402 is passed through to ports 406 and 408, and the effective multiplication value is two. When both D₁ and D₂ are LOW, the currents at all of the currents from V-I converter 402 are passed through current multiplier 404, and the effective multiplication is three. In this way, 2-bit multiplication is realized.

[0030] Note that the difference in voltages at nodes 414 and 416 represent the multiplication, where the currents at ports 406 and 408 are fed into resistive loads 418. In practice, loads 418 may be realized by active devices, to be described later. If the voltage at node 414 subtracted from the voltage at node 416 represent a weight, then a weight having the opposite sign is realized by subtracting the voltage at node 416 from the voltage at node 414. Also, it is to be noted that the channel width-to-length ratios for the pMOSFETs used in the current multiplier need not be powers of two. That is, it is not necessary that multiplication be performed in binary arithmetic. More generally, a mapping is provided between control signals and currents passed through the current multiplier, and it is not necessary that this mapping represent any particular arithmetic.

[0031] The combination of the V-I converter and current multiplier in FIG. 4 realizes a weighting of the input differential voltage to the V-I converter. This combination of V-I converter and current multiplier, along with loads 418, are realized as a single stage. Utilizing a single stage helps in filtering high data rate signals. A plurality of such combinations may be employed to realize a FIR (Finite Impulse Response) filter. For example, consider a FIR filter realized in FIG. 5. Input ports 502 and 504 receive an input differential voltage from a transmission line, such as that illustrated in FIG. 2. Sample-and-Hold (SH) circuits 506 a-d sample and hold the received differential signal. For simplicity, each SH circuit in FIG. 5 is shown as two switches (e.g., pass gates), each connected to a capacitor to store the received differential voltage. Other embodiments may employ other types of SH circuits. A clock phase generator 507 provides clock signals at various phases for each SH circuit. The clocking of the SH circuit will be described later. Each SH circuit is followed by one of V-I converters 508 a-d. Each V-I converter is followed by one of current multipliers 510 a-d. Each current multiplier has a set of control voltages to perform the suitable weighting (current multiplication). That is, a set of control voltages denoted by D_(a) is applied to current multiplier 510 a. Similar statements apply to the other current multipliers. Each current multiplier is followed by one of switches 512 a-d. These switches are two-by-two crossbar switches, so that for each switch, one of the two input ports is connected to one of the two output ports, with the other input port connected to the other output port. In this way, sign information is realized, as discussed with respect to FIG. 4. Current is sunk into loads 514 and 516, which are shown as simple resistors in FIG. 5. (Another embodiment for the loads is described later.) The voltages developed at nodes 518 and 520 are sensed by differential latch 522, which provides a logic signal at output port 524 indicative of the voltage difference at nodes 518 and 520.

[0032] The analog FIR filtering is represented by the differential voltage at nodes 518 and 520. Differential latch 522 effectively performs a decision, converting the analog information represented by the voltages at nodes 518 and 520 into a logic signal, indicative of whether a “1” or “0” was most likely transmitted. To account for “pre-cursors” and “post-cursors”, where a received signal at time t has inter-symbol interference from signals representing bit-times at times earlier and later than t, the logic signal provided by the differential latch at some time t may represent an estimate of the transmitted signal at a time earlier to t. That is, if s[i] is the received sequence, where i is an integer index representing time in some appropriate unit, then the filter weights may be synthesized such that the differential latch output at time n is an estimate of the transmitted bit at time n-m, where m is an integer.

[0033] In the embodiment of FIG. 5, a FIR filter of order 2 is realized. At any given bit-time, say at time t=n where n is an integer, one of the SH circuits has its switches closed to provide the next sample, say s[n+1], whereas the other three SH circuits hold the three most recent samples, s[n], s[n−1], and s[n−2]. Control signals are provided to the current multipliers corresponding to the three most recent samples to effectuate the FIR filtering, and the control signals for the current multiplier corresponding to the next sample s[n+1] are such that zero weighting is applied because s[n+1] is not yet completely acquired. At the next bit-time, t=n+1, the sample s[n+1] is available, the control signals are rotated (circularly shifted) with respect to the current multipliers, and the SH circuit corresponding to the next sample s[n+2] has its switches closed. This process is repeated each bit-time, where the timing of the SH circuits is such that only one of them has its switches closed during a bit-time, and the control voltages are circularly shifted from one current multiplier to the next in a sequential manner.

[0034] The above description regarding the timing of the sample-and-hold operations and the shifting of control signals for the embodiment of FIG. 5 is perhaps best made clear by considering FIGS. 6a through 6 d. In FIGS. 6a-d, FIR filtering is abstracted to multiplication units followed by a summer unit. A multiplication unit comprises a V-I converter and a current multiplier. A multiplication unit may be referred to as either a filter tap, or simply a multiplier. The filter weights are denoted by h[0], h[1], and h[2]. (For simplicity, FIGS. 6a-d show single-ended signaling, but its generalization to differential signaling should be obvious to one of ordinary skill in the relevant art.)

[0035] In FIG. 6a, the time index is t=n, and switch 602 is closed to acquire the next sample, s[n+1], from input-output (I/O) pad 601. Switches 604, 606, and 608 have already acquired samples s[n−2], s[n−1], and s[n], respectively. The weight for multiplier 610 is zero because switch 602 is in the process of acquiring sample s[n+1]. The weights for multipliers 612, 614, and 616 are the filter weights h[2], h[1], and h[0], respectively. The analog filtered output is provided by summer 618.

[0036] For FIG. 6b, the time index is t=n+1, and switch 602 is now opened because it has acquired sample s[n+1]. Switch 604 is now closed to acquire the next sample, s[n+2], and a zero weight is applied to its corresponding multiplier, 612. The filter weights have been circularly shifted when compared to FIG. 6a, where weight h[0] is applied to multiplier 610, and weights h[2] and [1] are applied to multipliers 614 and 616, respectively. In FIG. 6c, the time index is t=n+2, and switch 606 is closed to acquire the next sample, s[n+3]. Comparing FIG. 6c to FIG. 6b, it is seen that the filter weights have again been circularly shifted. In FIG. 6d, the time index is t=n+3, switch 608 is closed to acquire the next sample, s[n+4], and the weights have again been circularly shifted. The cycle indicated by FIGS. 6a-d is repeated. In this way, convolution is performed, where at each bit time, one of the SH circuits is acquiring the next sample, and the filter weights are circularly shifted to effectuate the convolution.

[0037] Note from FIGS. 6a-d that the sequence of switching the SH circuits and the sequence of applying the filter weights is such that circular shifting is employed. However, any repeating sequence for switching and shifting may be utilized, so long as the filter weights are applied to the appropriate multipliers at the appropriate time to effectuate the correct convolution.

[0038] As the filter weights are shifted to various multipliers, it may be necessary to control switches 512 a-d to account for the sign of the shifted weights. The control of switches 512 a-d, as well as the timing of SH circuits 507 and the shifting of control voltages to current multipliers 510 a-d, may be implemented by finite state machine 526. Other methods may be employed, for example, a memory table may be used to store the control signals.

[0039] In the particular embodiment of FIG. 5, switches 512 a-d were placed after current multipliers 510 a-d. However, because of linearity, it is to be noted that switches 512 a-d may be placed elsewhere in the sub-circuit “chains”. For example, these switches may be placed before the SH circuits, before the V-I converters, or before the current multipliers.

[0040] The presence of switches 512 a-d for implementing sign changes and the shifting of filter weights among the various filter taps adds to system complexity. However, filter structures may be employed where the multipliers are repeated, so that switches 512 a-d are not required and the filter weights need not be shifted.

[0041] Indeed, note that FIGS. 6a-d show four time “snapshots” of the filter weight positions. Inspection of FIGS. 6a-d results in the filter structure of FIG. 7. In FIG. 7, SH circuits 702 a-d are switched in a sequential manner, so that one of them is closed during any given bit duration to acquire the next sample, where the other three have already required the three most recent samples. Switch 704 is also switched among ports 706 a-d every bit time to provide the filtered output. (Again, for simplicity, the filter structure of FIG. 7 is single-ended, but its generalization to differential signaling should be obvious.)

[0042] For example, if SH circuits 702 a-c have acquired their respective samples and SH circuit 702 d is closed to acquire the next sample, then multipliers 708 a-c and summer 708 d provide the filtered output to port 706 a, and switch 704 switches to port 706 a. At the next bit time, SH circuit 702 a closes to acquire the next sample, and SH circuits 702 b-d have acquired the next most three recent samples, so that multipliers 710 a-b and summer 710 d provided the filtered output at port 706 b. This process continues, providing a filtered output at port 706 c and then next at port 706 c, and then the process repeats itself.

[0043] The filter structure of FIG. 7 may be viewed as comprising four sub-filters. For example, multipliers 708 a-c and summer 708 d together provide one of the four sub-filters. A summer associated with a sub-filter may be operated at a rate slower than a bit-time. For example, when SH circuit 702 c has acquired a sample, taps 708 a-c have one bit-time to process data before switch 702 a is closed to begin another acquisition. However, provided the differential latch in summer 708 d has begun evaluation after one bit-time, it may be given further time to complete its evaluation to provide its output logic signal, up to a total of 4 bit-times.

[0044] The filter structure of FIG. 8 is similar to that of FIG. 7, except that another SH circuit has been added. The operation of the filter in FIG. 8 is similar to that of FIG. 7, and not be repeated. However, because another SH circuit has been added, these SH circuits may be closed for 2 bit-times before opening to acquire a sample. These time intervals are overlapped, so that for any given bit-time duration, two SH circuits are closed. As a result, the filter structure for FIG. 8 may operate at a higher data rate than that of FIG. 7 for the same process technology.

[0045] The filter structures of FIG. 7 and 8 avoid the use of a finite state machine for shifting weights and the use of switches of the type 512 a-d at the expense of repeating filter taps. For many applications, the filter weights alternate in sign. For such applications, a filter structure may be utilized with less multipliers than the structures of FIG. 7 and 8, without the need for switches of the type 512 a-d, where filter weight shifting involving like-signed filter weights is used. Before describing in a general way such filter structures, it is pedagogically simpler to first consider an embodiment FIR filter of order 2 as shown in FIG. 9.

[0046] The filter structure of FIG. 9 shows two banks of SH circuits and taps. It is assumed that filter weights h[0] and h[2] are of one sign, and h[1] is of the opposite sign. Next to each tap is a set of filter weights indicating a sequence of filter weights shifted to that tap. For example, the sequence shifted into tap(1) is denoted by {h[0],h[2],0}, which means that the repeating sequence of filter weights . . . h[0], h[2], 0, h[0], h[2], 0, . . . shifted to tap(1). Note that the algebraic sign of the filter weights shifted to any one tap does not change, so that switches of the type 512 a-d are note needed. (The sign for 0 may be taken as either positive or negative.)

[0047] The timing of the filter weights and SH circuits in FIG. 9 may be explained by referring to FIG. 10. For each indicated tap in FIG. 10, its corresponding timing signal indicates when the corresponding SH circuit is closed (in the processing of acquiring a new sample) and when it is opened (a sample has been acquired and is held). A HIGH signal indicates that a SH circuit is closed, and a LOW signal indicates that a SH circuit is open. The actual acquisition time is indicated by a falling edge of the timing signal. Time is in reference to bit-times, as indicated at the bottom of FIG. 10. Without loss of generality, the bit-times are numbered as indicated. The weight is zero when the SH circuit is closed, otherwise, the weight is indicated next to the timing signal. A SH circuit is closed for a duration of two bit-times. The time duration for each filter weight is two bit-times.

[0048] For example, referring to the timing signal corresponding to tap(1), it is seen that the sample s[1] is acquired at bit-time 1 when the timing signal transitions from HIGH to LOW. At bit-time 1, the weight applied to tap(1) is h[0], for a duration of two bit-times. At bit-time 3, the weight h[2] is applied to tap(1), for a duration of two bit-times. The bit-time 5, the SH circuit closes for a duration of two bit times. At bit time 7, the SH circuit opens again to acquire sample s[7]. This process repeats, as indicated in FIG. 10.

[0049] At bit-time 3, samples s[1], s[2], and s[3] have been acquired and are available for tap(1), tap(2), and tap(3), respectively. Note that at bit-time 3, filter weight h[0] is being applied to tap(3), filter weight [1] is being applied to tap(2), and filter weight [2] is being applied to tap(1). Multiplication of the filter weights with their corresponding sampled data, followed by summing, results in h[0]s[3]+h[1]s[2]+h[2]s[3], which is the desired filtered output at bit-time 3. (Note that at bit-time 3, a weight of zero is applied to tap(4) and tap(5), so that they do not contribute to the filtered output.)

[0050] Inspection of FIG. 10 shows that the desired filtered output is available at every other bit-time, namely, bit-times 3, 5, 7, 9, 11, etc. Consequently, every other filtered output is provided at output port 902 in FIG. 9 at every other bit-time. The timing for the SH circuits and taps on the right hand side of FIG. 9 is identical to that of the left hand side, except that its operation is shifted one bit-time. Consequently, each filtered output is obtained by alternately sampling output ports 902 and 904.

[0051] From the above description for FIG. 9, it is seen that each SH circuit need only operate at ½ the bit-rate, and that filtered weights need only be shifted at ½ the bit rate. Furthermore, because each output port is sampled at every other bit-time, the differential latch associated with each summer may operate at ½ the bit-rate. Note that the number of taps for the filter structure of FIG. 9 is less than for the filter structure of FIG. 8, and that only two differential latches are employed. Furthermore, the gate capacitance seen by each SH circuit is less for the filter structure of FIG. 9.

[0052] The filter structure of FIG. 9 and its timing operation in FIG. 10 may be generalized to any order filter in which the filter weights alternate in sign, as will now be described. However, before beginning this generalization, some discussion of notation is in order. For simplicity of describing how the sequences are constructed, the sequences are assumed to be one-sided. That is, for any given sequence, there is a first member of the sequence, but not a last member. A one-sided sequence is described by listing an ordered set of elements, such as for example {a,b}, where a and b are variables or constants, which are then repeated in order to generate the sequence. In practice, however, all sequences are really finite in length, so that in the following description and claims, it is to be realized that all sequences used in actual embodiments end when the filter is no longer operated. It is only for simplicity of description and claiming that sequences are treated as one-sided and infinite in length.

[0053] Furthermore, for notational simplicity, it is convenient to introduce a weight denoted as NULL. The value of the NULL weight when used by a tap is taken to be zero. The NULL weight is introduced so as to distinguish it from an arbitrary weight, which may just happen to have a value of zero. This distinction is convenient, for in the following description, it is described that a SH circuit opens when the weight to its corresponding tap transitions from the NULL weight to some other weight. But it may happen that the weight transitions from the NULL weight to a weight having a zero value. This distinction between the NULL weight and an arbitrary weight, which may be zero, avoids ambiguity. We now begin with a generalization to the embodiment of FIG. 9 and the timing diagram of FIG. 10.

[0054] Let the filter weights for a filter of order N−1 be denoted by h[i], i=0, 1, . . . , N−1. There are two banks of SH circuits and taps, each followed by a summer having an output port. Each bank comprises N+2 SH circuits and taps. For a first bank of SH circuits and taps, label the taps as tap(i), i=1, 2, 3, . . . , N+2. The weight sequences shifted into each tap may be constructed as follows. Let h_(even) denote the ordered set of weights obtained by listing in order only and all of the even-indexed filter weights (0 is taken as an even index), and let h_(odd) denote the ordered set of weights obtained by listing in order only and all of the odd-indexed filter weights. Tap(1) has shifted to it the sequence of weights obtained by repeating in order the weights {h_(even), NULL}. Each weight in the sequence is shifted in at ½ the bit rate. Without loss of generality, let the first weight to tap(1), h[0], be shifted in at bit-time 1. Tap(2) has shifted to it the sequence of weights obtained by repeating in order the weights {h_(odd), NULL}, where the first weight, h[1], is shifted in at bit-time 2.

[0055] Sequences for the other taps are easily described in terms of the two sequences for tap(1) and tap(2). For tap(2 j+1) (odd-indexed taps), the sequence of weights is the same as for tap(1), except delayed in time by 2 j bit-times. For example, the sequence of weights for tap(3) is the sequence obtained by repeating {h_(even), NULL}, where the first weight, h[0], is shifted in at bit-time 2. For tap(2 j) (even-indexed taps), the sequence of weights is the same as for tap(2), except delayed in time by 2 j bit-times.

[0056] Each SH circuit is in its acquisition mode (closed) when the weight to its corresponding tap is the NULL weight. When the weight to a tap transitions from the NULL weight, its corresponding SH circuit opens to sample. An acquisition mode lasts for two bit-times because the weights for any tap are shifted in at I₂ the bit rate.

[0057] The second bank of SH circuits and taps are operated in identical fashion to the first bank, except that all timing is delayed by one bit-time. The filtered output are obtained by alternately sampling the output ports, where each output port is sampled at ½ the bit rate.

[0058] Referring back to FIG. 5, the combination of resistive loads 514 and 516, and differential latch 522, may be realized by the embodiment of FIG. 11, which may be referred to as an active cascode differential latch. nMOSFETs 1114 and 1116 play the role of active cascode transistors, although they are not cascode transistors in the classical sense because their gate voltages are not biased to a constant voltage. Input port 1102 is connected to one of nodes 518 and 520, and input port 1104 is connected to the other node. A clock signal in FIG. 11 is denoted by φ. When clock signal φ is HIGH, pre-charge transistor 1122 provides a low impedance path between the gates of transistors 1110 and 1112, pre-charging the differential latch so that the output voltages at output ports 1106 and 1108 are forced to be substantially equal to one another. When clock signal φ is LOW, pre-charge transistor 1122 switches OFF to put the differential latch in an evaluation mode, where a differential voltage at output ports 1106 and 1108 develops in response to the currents (or voltages) at input ports 1102 and 1104.

[0059] If more current is sourced to input port 1102 than is sourced to input port 1104, then the output voltage at output port 1106 increases, and the output voltage at output port 1108 decreases. Cross coupled pMOSFETs 1118 and 1120 are connected as a latch, so that the differential voltage developed at output ports 1106 and 1108 is amplified to a logic level.

[0060] The evaluation phase of the differential latch may begin at or just after a bit-time. For example, referring to the timing diagram of FIG. 10, evaluation phases for the differential latch on the left hand side bank in FIG. 9 may begin at odd-indexed bit-times. Consider an evaluation phase beginning at bit-time 3, for example. The filter weight h[0] is available at tap(3) for two bit-times, and the filter weight h[2] is available at tap(1) for two-bit times. However, at bit-time 3, the filter weight h[1] is available at tap(2) for only one more bit-time. Consequently, the differential latch should be designed so that it at least starts to settle to one of its two stable states within one bit time, i.e., a differential voltage starts to develop at output ports 1106 and 1108. At bit-time 4, the NULL weight is provided to tap(2). However, this shouldn't effect the output logic value of the differential latch even if it has not completely evaluated by bit-time 4 because at least a differential voltage has developed. However, before bit-time 5, the differential latch should completely evaluate with enough time left for the pre-charge phase to start and complete by bit-time 5. The entire cycle of an evaluation phase and a pre-charge phase should be no longer than two bit-times for the embodiment represented by FIGS. 9 and 10, as well as its generalization to other embodiments.

[0061] An argument similar to that which was made with respect to FIG. 3 shows that device sizes may be easily chosen such that nMOSFETs 1110 and 1112 operate in their triode regions and nMOSFETs 1114 and 1116 operate in their active regions. With nMOSFETs 1110 and 1112 operating in their triode regions, the differential latch of FIG. 11 has a relatively low input impedance, and furthermore, these nMOSFETs require a relatively small amount of headroom voltage. This may be important as supply voltages are scaled lower and lower, because voltage headroom for analog circuit blocks may be a critical issue. A small headroom voltage requirement also improves the input common-mode voltage range of the stages previous to the differential latch, i.e., the V-I converters and current multipliers.

[0062] The differential latch of FIG. 11 has applications other than for analog filters. More generally, the differential latch of FIG. 11 may find utility for other applications in which a low input impedance is desired for a differential latch having a relatively large common-mode voltage range. For example, the comparator of FIG. 12 utilizes the differential latch of FIG. 11. The differential output voltage at output ports 1202 and 1204 reach one of two logic levels depending upon the differential voltage at input ports 1206 and 1208, which are applied to the gates of pMOSFETs 1210 and 1212.

[0063] Many modifications and variations of the disclosed embodiments may be practiced without departing from the scope of the invention as claimed below. For example, given an analog circuit with current sources, pMOSFETs, and nMOSFETs, it is well known that a “dual” or “complementary” circuit exhibiting a similar operation may be synthesized by using current sinks in place of current sources, nMOSFETs in place of pMOSFETs, and pMOSFETs in place of nMOSFETs. As a particular example, consider the V-I converter circuit in FIG. 13, which is the complementary circuit to FIG. 3. By comparing FIG. 13 with FIG. 3, it is easily seen that the operation of the circuit of FIG. 13 is similar to that of FIG. 3, where nMOSFETs 1308, 1310, 1312, and 1314 take the role of pMOSFETs 308, 310, 312, and 314, respectively, and current sink 1306 takes the role of current source 306. Similar modifications may be made to all the disclosed circuits. Consequently, it is to be understood in the claims below that the term “current source” may also mean a “current sink”, and that to recite that current is sourced may also mean that the current is sunk.

[0064] FIR filtering may be employed using other embodiments of V-I converters. Referring to FIG. 3, pMOSFETs 310 and 314 may be degenerated in a different manner than using pMOSFETs 308 and 312, respectively, as shown. For example, in FIG. 14, diode-connected pMOSFETs 1402 and 1404 degenerate, respectively, pMOSFETs 1406 and 1408. In other embodiments, resistors may be used for degeneration, or perhaps cascode transistors having their gates at some fixed potential.

[0065] Another embodiment of a V-I converter is shown in FIG. 15. The gates of pMOSFETs 1510 and 1514 are connected to input ports 1502 and 1504, respectively. pMOSFET 1508 degenerates pMOSFET 1510, and pMOSFET 1512 degenerates pMOSFET 1514. For the embodiment of FIG. 15, pMOSFETs 1508 and 1512 operate in their triode regions. Current source 1506 provides bias current to the various pMOSFETs. Capacitor 1516 has one terminal connected to input port 1502, and its other terminal connected to the gates of pMOSFETs 1508 and 1512. Similarly, capacitor 1518 has one terminal connected to input port 1504, and its other terminal connected to the gates of pMOSFETs 1508 and 1512. pMOSFET 1520 is diode-connected with its gate connected to its drain, and its source connected to the gates of pMOSFETs 1508 and 1512. The small-signal equivalent of diode-connected pMOSFET 1520 is a resistor, thus providing an small-signal resistive path between the gates of pMOSFETs 1512 and the substrate (or ground).

[0066] The combination of capacitors 1516 and 1518, and pMOSFET 1520, provides a common-mode high-pass filter from input ports 1502 and 1504 to the gates of pMOSFETs 1508 and 1512. Common-mode voltage variations at input ports 1502 and 1504 are high-pass filtered to the gates of degenerating pMOSFETs 1508 and 1512 so that variations in their gate-to-source voltages are reduced. This may be argued heuristically as follows. With the gates of pMOSFETs 1510 and 1514 connected to input ports 1502 and 1504, respectively, a common-mode variation in the input voltages causes approximately the same common-mode variation in voltages at the sources of pMOSFETs 1510 and 1514 because the total current is fixed by current source 1506. With degenerating pMOSFETs 1508 and 1512 operating in their triodes regions and their drains connected to the sources of pMOSFETs 1510 and 1514, respectively, there is also the same common-mode variation at the sources of degenerating pMOSFETs 1508 and 1512 because the total current is fixed. By providing common-mode high-pass filtering from input ports 1510 and 1514 to the gates of degenerating pMOSFETs 1508 and 1512, the same common-mode variation is seen by the gates of degenerating pMOSFETs 1508 and 1512 as is seen by their sources, so that common-mode variations in their gate-to-source voltages are reduced.

[0067] With degenerating pMOSFETs 1508 and 1512 operating in their triode regions, variations in their small-signal resistances are reduced if common-mode variations in their gate-to-source voltages are reduced. By reducing variations in their small-signal resistances, there is less common-mode variation in the V-I converter of FIG. 15. This is expected to improve the common-mode rejection of the V-I converter, as well as a discrete-time filter employing such a V-I converter.

[0068] For some embodiments, capacitors 1516 and 1518 may also be used as sampling capacitors. The effective RC time constant may be acceptable because the impedance of the channel (e.g., transmission lines 206 and 208 in FIG. 2) is in parallel with the impedance of pMOSFET 1520. For some embodiments, a resistor may be used in place of pMOSFET 1520.

[0069] Another embodiment of the present invention utilizing a folded tap design is shown in FIG. 16. For simplicity, only one tap with a 2-bit multiplier, along with a differential latch, is shown. It should be clear how to generalize to more than one tap, and to multipliers having more than two bits of resolution. The use of an active current mirror, such as active current mirror 1602, allows for a folded architecture. The tap in FIG. 16 may be viewed as comprising two stages, where the first stage comprises V-I converter 1604, and the second stage comprises active current mirror 1602 and multiplier 1606. Other embodiments of V-I converters may be used instead of the particular embodiment of V-I converter 1604, such as the V-I converter of FIGS. 3, 14, or 15, for example. Multiplier 1606 is the dual of multiplier 404, where nMOSFETs are used for the multiplier 1606. Its operation is essentially the same as the operation of multiplier 404, where now current is shunted to a voltage potential higher than ground (substrate). Because of the similarity of multiplier 1606 with multiplier 404, a separate discussion of its operation need not be given. Similarly, differential latch 1608 is the dual of differential latch FIG. 11. Its operation is essentially the same as the differential latch of FIG. 11, and so a separate discussion need not be given.

[0070] Active current mirror 1602 comprises nMOSFETs 1610 and 1612, which are operated in their triode regions, and nMOSFETs 1614 and 1616, which are operated in their active regions. The gates of nMOSFETs 1610, 1612, 1614, and 1616 are at some bias potential V_(B). Active current mirror 1610 sources (sinks) variations in currents to multiplier 1606 that are proportional to variations in currents sourced by V-I converter 1604 to nodes 1618 and 1620. This may heuristically be argued as follows. Suppose current I₊ sourced by V-I converter 1604 to node 1620 increases above its nominal value. (This nominal value is one-half the current sourced by current source 1605, i.e., the source-drain currents of pMOSFETs 1607 and 1609 when the input voltages V₊ and V⁻ are equal to each other.) Suppose also that current I⁻ sourced by V-I converter 1604 to node 1618 decreases below its nominal value. With nMOSFET 1612 in its triode region, an increase in I₊ at node 1620 raises the voltage at node 1620, which reduces the gate-to-source voltage of nMOSFET 1616, which in turn reduces the source-drain current of nMOSFET 1616 sourced to multiplier 1606. Similarly, with nMOSFET 1610 in its triode region, a decrease in I⁻ at node 1618 decreases the voltage at node 1618, which increases the gate-to-source voltage of nMOSFET 1614, which in turn increases the source-drain current of nMOSFET 1614 sourced to multiplier 1606.

[0071] The above statements regarding variations in currents may be made more precise as follows. Let ΔI₊ denote the differential of current I₊ about its nominal value. That is, ΔI₊ is the variation in current sourced by V-I converter 1604 to node 1620. Similarly, let ΔI⁻ denote the differential of current I₊. The current sourced by nMOSFET 1616 to multiplier 1606 may be written as I_(DC)−ωΔI₊, where ω is a positive weight and I_(DC) is a bias current. Consequently, the variation in current sourced by nMOSFET 1616 to multiplier 1606 is −ωΔI₊. Similarly, the current sourced by nMOSFET 1614 to multiplier 1606 may be written as I_(DC)−ωΔI⁻, and consequently the variation in current sourced by nMOSFET 1614 to multiplier 1606 is −ωΔI⁻. The variations in currents sourced by active current mirror 1602 to multiplier 1606 are seen to be opposite in sign to the variations in currents sourced by V-I converter 1604 to nodes 1620 and 1618. This is the reason why the voltages at output ports 1622 and 1624 of differential latch 1608 are denoted respectively as V_(OUT)⁻

[0072] and V_(OUT)⁺.

[0073] The above discussion regarding small-signal currents may be restated as follows. The differential current sourced by V-I converter 1604 to nodes 1614 and 1616 may be defined as the difference i≡(I₊−I⁻). Assuming that ΔI₊=−ΔI⁻, which is a reasonable assumption, then i=2ΔI₊. Similarly, the differential current sourced by active current mirror 1602, denoted as i_(CM), may be defined as the difference in the source-drain currents of nMOSFETs 1616 and 1614. Consequently, from the previous expressions for these source-drain currents, it follows that i_(CM)=−2ωΔI₊=−ωi. That is, the differential current sourced by active current mirror 1602 to current multiplier 1606 is proportional to the differential current sourced by V-I converter 1604 to active current mirror 1602. The proportionality factor is −ω, where its numerical value depends upon the operating characteristics of nMOSFETs 1602, 1612, 1614, and 1616.

[0074] The folded architecture of FIG. 16 comprises two stages, whereas the tap architecture of FIG. 4 has the V-I converter and current multiplier in only one stage. The tap of FIG. 4 is expected to be faster than the folded architecture of FIG. 16. However, the folded architecture is expected to achieve a larger input voltage headroom. As a result, the folded architecture may be more suited to smaller ranges of input voltages.

[0075] The use of an active current mirror allows for controlling of the DC bias current by adjusting the bias voltage on the gates of transistors 1610, 1612, 1614, and 1616. Furthermore, the linearity of the voltage-to-current converter is improved.

[0076] It should further be appreciated that the invention claimed below is not necessarily limited to differential signaling. For example, pseudo-differential signaling may be employed, in which a voltage reference is transmitted along with a single-ended signal, or perhaps is generated at the receiver end. In this case, one of the input ports to the V-I converters is fixed at the reference voltage. Consequently, it is to be understood that claiming a differential latch, or claiming a V-I converter with two input ports, does not necessarily imply that differential signaling is employed. 

What is claimed is:
 1. An analog filter comprising: a voltage-to-current converter to source a differential current; a current mirror coupled to the voltage-to-current converter to source a differential current proportional to the differential current sourced by the voltage-to-current converter; a current multiplier coupled to the current mirror to source a differential current proportional to the differential current sourced by the current mirror; and a differential latch coupled to the current multiplier to receive the differential current sourced by the current multiplier.
 2. The analog filter as set forth in claim 1, wherein the current mirror is an active current mirror.
 3. The analog filter as set forth in claim 2, the active current mirror comprising first, second, third, and fourth transistors each having a gate at a bias voltage.
 4. An analog filter comprising: a voltage-to-current converter comprising a first input port and a second input port, the voltage-to-current converter comprising: a first transistor comprising a gate connected to the first input port; and a second transistor comprising a gate connected to the second input port; wherein the first and second transistors source a differential current i; a current multiplier comprising a first output port and a second output port to shunt a weighted differential current (1−α)i_(CM) so as to pass a weighted differential current αi_(CM) to the first output port and the second output port, where α is a weight and where i_(CM) is a differential current proportional to i.
 5. The analog filter as set forth in claim 4, where i_(CM)=i.
 6. The analog filter as set forth in claim 4, further comprising: an active current mirror to load the voltage-to-current converter and to source to the current multiplier the differential current i_(CM).
 7. The analog filter as set forth in claim 6, wherein the first and second transistors of the voltage-to-current converter comprise drains, the active current mirror comprising: a first transistor comprising a gate and a drain connected to the drain of the first transistor of the voltage-to-current converter; a second transistor comprising a gate and a drain connected to the drain of the second transistor of the voltage-to-current converter; a third transistor comprising a gate and a source connected to the drain of the first transistor of the active current mirror; and a fourth transistor comprising a gate and a source connected to the drain of the second transistor of the active current mirror; wherein the gates of the first, second, third, and fourth transistors of the active current mirror are at a bias voltage.
 8. The analog filter as set forth in claim 4, the first and second transistors of the voltage-to-current converter comprising sources, the voltage-to-current converter further comprising: a third transistor comprising a gate and a drain connected to the source of the first transistor of the voltage-to-current converter; a fourth transistor comprising a gate and a drain connected to the source of the second transistor of the voltage-to-current converter; and a common-mode high-pass filter coupling the first and second input ports of the voltage-to-current converter to the gates of the third and fourth transistors of the voltage-to-current converter.
 9. A computer system comprising: a board comprising a first transmission line and a second transmission line; and a receiver coupled to the first and second transmission lines, the receiver comprising an analog filter, the analog filter comprising: a voltage-to-current converter comprising a first input port and a second input port, the voltage-to-current converter comprising: a first transistor comprising a gate connected to the first input port; and a second transistor comprising a gate connected to the second input port; wherein the first and second transistors source a differential current i; and a current multiplier comprising a first output port and a second output port to shunt a weighted differential current (1−α)i_(CM) so as to pass a weighted differential current αi_(CM) to the first output port and the second output port, where α is a weight and where i_(CM) is a differential current proportional to i.
 10. A voltage-to-current converter comprising: a first transistor to conduct a first current I₁ and comprising a gate connected to the first input port; a second transistor to conduct a second current I₂ and comprising a gate connected to the second input port; a third transistor coupled to the first transistor to conduct the first current I₁; a fourth transistor coupled to the second transistor to conduct the second current I₂; a current source to source a current I to the first and second transistors so that the sum of the first current I₁ and the second current I₂ is substantially equal to the current I; and a high-pass filter coupling the first input port and the second input port to the third and fourth transistors.
 11. The voltage-to-current converter as set forth in claim 10, wherein, the second transistor comprises a gate; the fourth transistor comprises a gate; and the high-pass filter comprises a first capacitor comprising a first terminal connected to the first input port and a second terminal connected to the gate of the third transistor; and a second capacitor comprising a first terminal connected to the second input port and a second terminal connected to the gate of the fourth transistor.
 12. The voltage-to-current converter as set forth in claim 11, wherein the high-pass filter further comprises a resistive device connected to the gates of the third and fourth transistors.
 13. The voltage-to-current converter as set forth in claim 12, wherein the resistive device comprises a diode connected transistor.
 14. An analog filter comprising a set of taps, tap(i), i=1, 2, . . . , n, where for each i=1, 2, . . . , n, tap(i) comprises: a voltage-to-current converter(i) comprising a first input port(i) and a second input port(i), the voltage-to-current converter(i) comprising: a first transistor to conduct a first current I₁(i) and comprising a gate connected to the first input port(i); a second transistor to conduct a second current I₂(i) and comprising a gate connected to the second input port(i); a third transistor coupled to the first transistor to conduct the first current I₁(i); a fourth transistor coupled to the second transistor to conduct the second current I₂(i); a current source(i) to source a current I(i) to the first and second transistors so that the sum of the first current I₁(i) and the second current I₂(i) is substantially equal to the current I(i); and a high-pass filter coupling the first input port(i) and the second input port(i) to the third and fourth transistors; and a current multiplier(i) comprising a first output port(i) and a second output port(i), and coupled to the voltage-to-current converter(i) to shunt a current [1−α(i)]I₁(i) so as to pass a first weighted current a(i)II(i) to the first output port(i) and to shunt a current [1−α(i)]I₂(i) so as to pass a second weighted current α(i)I₂(i) to the second output port(i), where α(i) is a weight.
 15. The analog filter as set forth in claim 14, wherein each current multiplier(i) further comprises: a first set(i) of parallel connected transistors, each with a gate, to shunt the current [1−α(i)]I₁(i); a second set(i) of parallel connected transistors, each with a gate, to pass the first weighted current α(i)I₁(i) to the first output port(i); a third set(i) of parallel connected transistors, each with a gate, to shunt the current [1−α(i)]I₂(i); and a fourth set(i) of parallel connected transistors, each with a gate, to pass the second weighted current α(i)I₂(i) to the second output port(i); wherein the weight α(i) is a function of at least a set of control voltages applied to the gates of the first set(i), the second set(i), the third set(i), and the fourth set(i).
 16. The analog filter as set forth in claim 15, the analog filter further comprising a differential latch comprising first and second input ports, the differential latch to provide an output logic signal indicative of whether or not the first input port of the differential latch sinks more current than the second input port of the differential latch, wherein for each i=1, 2, . . . , n, tap(i) sources α(i)I₁(i) to the first input port of the differential latch and sources α(i)I₂(i) to the second input port of the differential latch if i is even, and sources α(i) I₁(i) to the second input port of the differential latch and sources α(i)I₂(i) to the first input port of the differential latch if i is odd.
 17. The analog filter as set forth in claim 16, wherein the analog filter implements discrete-time filtering at a bit-rate r with filter weights h[j], j=0, 1, . . . , N−1, wherein n=N+2, where h_(even) denotes an ordered set of weights obtained by listing in order only and all of the absolute value of the even-indexed filter weights, and h_(odd) denotes an ordered set of weights obtained by listing in order only and all of the absolute value of the odd-indexed filter weights, the analog filter further comprising a finite state machine: to provide a set of control voltages to tap(1) so that α(1) is a sequence of weights obtained by repeating the ordered set of weights {h_(even), NULL}; to provide a set of control voltages to tap(2) so that α(2) is a sequence of weights obtained by repeating the ordered set of the weights {h_(odd), NULL}starting at one bit-time after the sequence of weights to tap(1); to provide a set of control voltages to tap(2 j+1) so that α(2 j+1) is a sequence of weights the same as for tap(1) except delayed in time by 2 j bit-times, where (2 j+1) runs over the odd-indexed taps; and to provide a set of control voltages to tap(2 j) so that α(2 j) is a sequence of weights the same as for tap(2) except delayed in time by 2 j bit-times, where (2 j) runs over the even-indexed taps.
 18. A computer system comprising: a board comprising a first transmission line and a second transmission line; and a receiver coupled to the first and second transmission lines, the receiver comprising an analog filter, the analog filter comprising a set of taps, tap(i), i=1, 2, . . . , n, where for each i=1, 2, . . . , n, tap(i) comprises: a voltage-to-current converter(i) comprising a first input port(i) and a second input port(i), the voltage-to-current converter(i) comprising: a first transistor to conduct a first current I₁(i) and comprising a gate connected to the first input port(i); a second transistor to conduct a second current I₂(i) and comprising a gate connected to the second input port(i); a third transistor coupled to the first transistor to conduct the first current I₁(i); a fourth transistor coupled to the second transistor to conduct the second current I₂(i); a current source(i) to source a current I(i) to the first and second transistors so that the sum of the first current I₁(i) and the second current I₂(i) is substantially equal to the current I(i); and a high-pass filter(i) coupling the first input port(i) and the second input port(i) to the third and fourth transistors; and a current multiplier(i) comprising a first output port(i) and a second output port(i), and coupled to the voltage-to-current converter(i) to shunt a current [1−α(i)]I₁(i) so as to pass a first weighted current α(i)I₁(i) to the first output port(i) and to shunt a current [1−α(i)]I₂(i) so as to pass a second weighted current α(i)I₂(i) to the second output port(i), where α(i) is a weight.
 19. The computer system as set forth in claim 18, wherein for each i=1, 2, . . . , n, the high-pass filter(i) comprises a first capacitor(i) and a second capacitor(i).
 20. The computer system as set forth in claim 19, wherein for each i=1, 2, . . . , n, the first capacitor(i) and the second capacitor(i) are sampling capacitors.
 21. An analog filter comprising a set of taps, tap(i), i=1, 2, . . . , n, where for each i=1, 2, . . . , n, tap(i) comprises: a voltage-to-current converter(i) comprising a first input port(i) and a second input port(i), the voltage-to-current converter(i) comprising: a first transistor to conduct a first current I₁(i) and comprising a gate connected to the first input port(i); a second transistor to conduct a second current I₂(i) and comprising a gate connected to the second input port(i); and a current source(i) to source a current I(i) to the first and second transistors so that the sum of the first current I₁(i) and the second current I₂(i) is substantially equal to the current I(i); an active current mirror(i) coupled to the voltage-to-current converter(i) to source currents I₃(i) and I₄(i), where I₃(i)≡(I_(DC)−ω(i)ΔI₁(i)) and I₄(i)=(I_(DC)−ω(i)ΔI₂(i)), where ω(i) is a weight, ΔI₁ (i) is the differential of I₁(i) with respect to its value when the first input port(i) and the second input port(i) are at a same voltage, and ΔI₂(i) is the differential of I₂(i) with respect to its value when the first input port(i) and the second input port(i) are at a same voltage, and I_(DC) is a bias current; and a current multiplier(i) comprising a first output port(i) and a second output port(i), and coupled to the active current mirror(i) to shunt a current (1−α(i))I₃(i) so as to pass a first weighted current α(i)I₃(i) to the first output port(i) and to shunt a current (1−α(i))I₄(i) so as to pass a second weighted current α(i)I₄(i) to the second output port(i), where α(i) is a weight.
 22. The analog filter as set forth in claim 21, wherein each current multiplier(i) further comprises: a first set(i) of parallel connected transistors, each with a gate, to shunt the current [1−α(i)]I₃(i); a second set(i) of parallel connected transistors, each with a gate, to pass the first weighted current α(i)I₃(i) to the first output port(i); a third set(i) of parallel connected transistors, each with a gate, to shunt the current [1−α(i)]I₄(i); and a fourth set(i) of parallel connected transistors, each with a gate, to pass the second weighted current α(i)I₄(i) to the second output port(i); wherein the weight α(i) is a function of at least a set of control voltages applied to the gates of the first set(i), the second set(i), the third set(i), and the fourth set(i).
 23. The analog filter as set forth in claim 22, the analog filter further comprising a differential latch comprising first and second input ports, the differential latch to provide an output logic signal indicative of whether or not the first input port of the differential latch sinks more current than the second input port of the differential latch, wherein for each i=1, 2, . . . , n, tap(i) sources α(i)I₃(i) to the first input port of the differential latch and sources α(i)I₄(i) to the second input port of the differential latch if i is even, and sources α(i)I₃(i) to the second input port of the differential latch and sources α(i)I₄(i) to the first input port of the differential latch if i is odd.
 24. The analog filter as set forth in claim 23, wherein the analog filter implements discrete-time filtering at a bit-rate r with filter weights h[j], j=0, 1, . . . , N−1, wherein n=N+2, where h_(even) denotes an ordered set of weights obtained by listing in order only and all of the absolute value of the even-indexed filter weights, and h_(odd) denotes an ordered set of weights obtained by listing in order only and all of the absolute value of the odd-indexed filter weights, the analog filter further comprising a finite state machine: to provide a set of control voltages to tap(1) so that α(1) is a sequence of weights obtained by repeating the ordered set of weights {h_(even), NULL}; to provide a set of control voltages to tap(2) so that α(2) is a sequence of weights obtained by repeating the ordered set of the weights {h_(odd), NULL}starting at one bit-time after the sequence of weights to tap(1); to provide a set of control voltages to tap(2 j+1) so that α(2 j+1) is a sequence of weights the same as for tap(1) except delayed in time by 2 j bit-times, where (2 j+1) runs over the odd-indexed taps; and to provide a set of control voltages to tap(2 j) so that α(2 j) is a sequence of weights the same as for tap(2) except delayed in time by 2 j bit-times, where (2 j) runs over the even-indexed taps.
 25. The analog filter as set forth in claim 24, wherein the set of control voltages are provided at a rate r/2.
 26. The analog filter as set forth in claim 25, further comprising a set of sample-and-hold circuits, SH circuit(i), i=1, 2, . . . , n, wherein for each i=1, 2, . . . , n, the SH circuit(i) is coupled to tap(i) to close when α(i) is NULL and to open when α(i) transitions from NULL to provide a sampled voltage from a first transmission line to the first input port(i) and a sampled voltage from a second transmission line to the second input port(i).
 27. The analog filter as set forth in claim 22, the analog filter further comprising a differential latch comprising first and second input ports, the differential latch to provide an output logic signal indicative of whether or not the first input port of the differential latch sinks more current than the second input port of the differential latch, wherein for each i=1, 2, . . . , n, tap(i) sources α(i)I₃(i) to the first input port of the differential latch and sources α(i)I₄(i) to the second input port of the differential latch.
 28. The analog filter as set forth in claim 22, wherein associated with each tap(i) is a weight s(i)α(i) where s(i) is either one or negative one, the analog filter further comprising a differential latch comprising first and second input ports, the differential latch to provide an output logic signal indicative of whether or not the first input port of the differential latch sinks more current than the second input port of the differential latch, wherein for each i=1, 2, . . . , n, α(i)I₃(i) is sourced to the first input port of the differential latch and α(i)I₄(i) is sourced to the second input port of the differential latch if s(i) is one, and α(i)I₃(i) is sourced to the second input port of the differential latch and α(i)I₄(i) is sourced to the first input port of the differential latch if s(i) is negative one.
 29. The analog filter as set forth in claim 28, further comprising a set of sample-and-hold circuits, SH circuit(i), i=1, 2, . . . , n, wherein for each i=1, 2, . . . , n, the SH circuit(i) is coupled to tap(i) to close when α(i) is NULL and to open when α(i) transitions from NULL so as to provide a sampled voltage from a first transmission line to the first input port(i) and a sampled voltage from a second transmission line to the second input port(i).
 30. The analog filter as set forth in claim 21, wherein for each i=1, 2, . . . , n, I(i)=I(1).
 31. The analog filter as set forth in claim 21, wherein for each i=1, 2, . . . , n, the voltage-to-current converter(i) further comprises first and second devices to degenerate, respectively, the first and second transistors of the voltage-to-current converter(i).
 32. The analog filter as set forth in claim 31, wherein for each i=1, 2, . . . , n, the current multiplier(i) further comprises: a first set(i) of parallel connected transistors, each with a gate, to shunt the current [1−α(i)]I₃(i); a second set(i) of parallel connected transistors, each with a gate, to pass the first weighted current α(i)I₃(i) to the first output port(i); a third set(i) of parallel connected transistors, each with a gate, to shunt the current [1−α(i)]I₄(i); and a fourth set(i) of parallel connected transistors, each with a gate, to pass the second weighted current α(i)I₄(i) to the second output port(i); wherein the weight α(i) is a function of at least a set of control voltages applied to the gates of the first set(i), the second set(i), the third set(i), and the fourth set(i).
 33. The analog filter as set forth in claim 32, the analog filter further comprising a differential latch comprising first and second input ports, the differential latch to provide an output logic signal indicative of whether or not the first input port of the differential latch sinks more current than the second input port of the differential latch, wherein for each i=1, 2, . . . , n, tap(i) sources α(i)I₃(i) to the first input port of the differential latch and sources α(i)I₄(i) to the second input port of the differential latch if i is even, and sources α(i)I₃(i) to the second input port of the differential latch and sources α(i)I₄(i) to the first input port of the differential latch if i is odd.
 34. The analog filter as set forth in claim 31, wherein for each i=1, 2, . . . , n, the first device to degenerate the first transistor of the voltage-to-current converter(i) is a transistor serially connected to the first transistor of the voltage-to-current converter(i), comprising a gate connected to the first input port(i); and the second device to degenerate the second transistor of the voltage-to-current converter(i) is a transistor serially connected to the second transistor of the voltage-to-current converter(i), comprising a gate connected to the second input port(i).
 35. The analog filter as set forth in claim 34, wherein for each i=1, 2, . . . , n, the current multiplier(i) further comprises: a first set(i) of parallel connected transistors, each with a gate, to shunt the current [1−α(i)]I₃(i); a second set(i) of parallel connected transistors, each with a gate, to pass the first weighted current α(i)I₃(i) to the first output port(i); a third set(i) of parallel connected transistors, each with a gate, to shunt the current [1−α(i)]I₄(i); and a fourth set(i) of parallel connected transistors, each with a gate, to pass the second weighted current α(i)I₄(i) to the second output port(i); wherein the weight α(i) is a function of at least a set of control voltages applied to the gates of the first set(i), the second set(i), the third set(i), and the fourth set(i).
 36. The analog filter as set forth in claim 31, wherein for each i=1, 2, . . . , n, the voltage-to-converter(i) further comprises a high-pass filter comprising a first capacitor comprising a first terminal connected to the first input port(i) and a second terminal connected to the first device to degenerate the first transistor of the voltage-to-current converter(i); and a second capacitor comprising a first terminal connected to the second input port(i) and a second terminal connected to the second device to degenerate the second transistor of the voltage-to-converter(i).
 37. The analog filter as set forth in claim 36, wherein for each i=1, 2, . . . , n, the current multiplier(i) further comprises: a first set(i) of parallel connected transistors, each with a gate, to shunt the current [1−α(i)]I₃(i); a second set(i) of parallel connected transistors, each with a gate, to pass the first weighted current α(i)I₃(i) to the first output port(i); a third set(i) of parallel connected transistors, each with a gate, to shunt the current [1−α(i)]I₄(i); and a fourth set(i) of parallel connected transistors, each with a gate, to pass the second weighted current α(i)I₄(i) to the second output port(i); wherein the weight α(i) is a function of at least a set of control voltages applied to the gates of the first set(i), the second set(i), the third set(i), and the fourth set(i).
 38. The analog filter as set forth in claim 22, the analog filter further comprising first and second loads, wherein for each i=1, 2, . . . , n, tap(i) sources α(i)I₃(i) to the first load and sources α(i)I₄(i) to the second load if i is even, and sources α(i)I₃(i) to the second load and sources α(i)I₄(i) to the first load if i is odd.
 39. The analog filter as set forth in claim 38, wherein for each i=1, 2, . . . , n, the voltage-to-current converter(i) further comprises first and second devices to degenerate, respectively, the first and second transistors of the voltage-to-current converter(i).
 40. An analog filter comprising a set of taps, tap(i), i=1, 2, . . . , n, where for each i=1, 2, . . . , n, tap(i) comprises: a voltage-to-current converter(i) comprising a first input port(i) and a second input port(i), the voltage-to-current converter(i) comprising: a first transistor comprising a source, a drain, and a gate connected to the first input port(i); a second transistor comprising a source, a drain, and a gate connected to the second input port(i); and a current source(i) to source current to the first and second transistors; an active current mirror(i) comprising: a first transistor comprising a gate and a drain connected to the drain of the first transistor of the voltage-to-current converter(i); a second transistor comprising a gate and a drain connected to the drain of the second transistor of the voltage-to-current converter(i); a third transistor comprising a gate, a source connected to the drain of the first transistor of the active current mirror(i), and a drain; and a fourth transistor comprising a gate, a source connected to the drain of the second transistor of the active current mirror(i), and a drain; wherein the gates of the first, second, third, and fourth transistors of the active current mirror(i) are at a bias voltage; and a current multiplier(i) comprising a first output port(i) and a second output port(i), the current multiplier(i) comprising: a first set of parallel connected transistors, transistor(1,i,j), j=1, 2, . . . , k(i), where for each j=1, 2, . . . , k(i), transistor(1,i,j) comprises a source connected to the drain of the third transistor of the active current mirror(i), and a gate at a logical voltage D(i,j)*, where D(i,j)* denotes the Boolean complement of D(i,j); a second set of parallel connected transistors, transistor(2,i,j), j=1, 2, . . . , k(i), where for each j=1, 2, . . . , k(i), transistor(2,i,j) comprises a source connected to the drain of the third transistor of the active current mirror(i), a drain connected to the first output port(i), and a gate at the voltage D(i,j); a third set of parallel connected transistors, transistor(3,i,j), j=1, 2, . . . , k(i), where for each j=1, 2, . . . , k(i), transistor(3,i,j) comprises a source connected to the drain of the fourth transistor of the active current mirror(i), and a gate at the voltage D(i,j)*; and a fourth set of parallel connected transistors, transistor(4,i,j), j=1, 2, . . . , k(i), where for each j=1, 2, . . . , k(i), transistor(4,i,j) comprises a source connected to the drain of the fourth transistor of the active current mirror(i), a drain connected to the second output port(i), and a gate at the voltage D(i,j).
 41. The analog filter as set forth in claim 40, where for each i=1, 2, . . . , n, the voltage-to-current converter(i) further comprises: a first device to degenerate the first transistor of the voltage-to-current converter(i); and a second device to degenerate the second transistor of the voltage-to-current converter(i).
 42. The analog filter as set forth in claim 40, wherein for each i=1, 2, . . . , n, k(i)=k(1), and D(i,j)=D(1,j) for each j=1, 2, . . . , k(1).
 43. A computer system comprising: a board comprising a first transmission line and a second transmission line; and a receiver coupled to the first and second transmission lines, the receiver comprising an analog filter, the analog filter comprising a set of taps, tap(i), i=1, 2, . . . , n, where for each i=1, 2, . . . , n, tap(i) comprises: a voltage-to-current converter(i) comprising a first input port(i) and a second input port(i), the voltage-to-current converter(i) comprising: a first transistor to conduct a first current I₁(i) and comprising a gate connected to the first input port(i); a second transistor to conduct a second current I₂(i) and comprising a gate connected to the second input port(i); and a current source(i) to source a current I(i) to the first and second transistors so that the sum of the first current I₁(i) and the second current I₂(i) is substantially equal to the current I(i); an active current mirror(i) coupled to the voltage-to-current converter(i) to source currents I₃(i) and I₄(i), where I₃(i)≡(I_(DC)−ω(i)ΔI₁(i)) and I₄(i)=(I_(DC)−ω(i)ΔI₂(i)), where ω(i) is a weight, ΔI₁ (i) is the differential of I₁(i) with respect to its value when the first input port(i) and the second input port(i) are at a same voltage, and ΔI₂(i) is the differential of I₂(i) with respect to its value when the first input port(i) and the second input port(i) are at a same voltage, and I_(DC) is a bias current; and a current multiplier(i) comprising a first output port(i) and a second output port(i), and coupled to the active current mirror(i) to shunt a current (1−α(i))I₃(i) so as to pass a first weighted current α(i)I₃(i) to the first output port(i) and to shunt a current (1−α(i))₄(i) so as to pass a second weighted current (α(i)I₄(i) to the second output port(i), where α(i) is a weight.
 44. A computer system comprising: a board comprising a first transmission line and a second transmission line; and a receiver coupled to the first and second transmission lines, the receiver comprising an analog filter, the analog filter comprising a voltage-to-current converter, the voltage-to-current converter comprising: a first transistor to conduct a first current I₁ and comprising a gate connected to the first input port; a second transistor to conduct a second current I₂ and comprising a gate connected to the second input port; a third transistor coupled to the first transistor to conduct the first current I₁; a fourth transistor coupled to the second transistor to conduct the second current I₂; a current source to source a current I to the first and second transistors so that the sum of the first current I₁ and the second current I₂ is substantially equal to the current I; and a high-pass filter coupling the first input port and the second input port to the third and fourth transistors. 